Design a traffic light controller for the intersection of streets A and B$.$

Sa $=1$: when a vehicle is approaching on street A; Sb $=1$: when a vehicle is approaching on street B$.$

Street A has a green light until a vehicle approaches on street B$.$

Ga$,$ Ya$,$ and Ra control green, yellow and red street A lights respectively; Gb$,$ Yb$,$ and Rb control green, yellow and red street B lights respectively.

Use a modulo $6$ counter with additional logic implemented on a Programmable Logic Array $($PLA$).$

a$)$ Using Karnaugh maps or otherwise, define the Boolean expressions required to generate each of the traffic light control signals, minimising the resource used in the PLA. $(6)$

b$)$ Suggest appropriate control signals for the counter such that the counter increments every clock cycle with two exceptions as shown in the state graph of Figure B$3$b$.$ Define the Boolean expressions required to drive these control signals. $(3)$

c$)$ Sketch the PLA table required to implement the combinational logic functionality. $(6)$